Related papers: An Introduction to Quantum Chaos
Mesoscopic devices, with system sizes in the range of several to several dozens wavelengths, represent paradigmatic model systems for the observation of quantum chaotic behaviour based on semiclassical concepts. Those electronic and…
The notion of Shannon entropy is crucial for the theory of classical information. In quantum information theory, an analogous key role is played by the von Neumann entropy: quantum information processing is closely related to entropy…
The problem of Turing pattern formation has attracted much attention in nonlinear science as well as physics, chemistry and biology. So far all Turing patterns have been observed in stationary and oscillatory media only. In this letter we…
A non-classical, non-quantum theory, or NCQ, is any fully consistent theory that differs fundamentally from both the corresponding classical and quantum theories, while exhibiting certain features common to both. Such theories are of…
Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions…
A new formulation of the theory of quantum mechanical multichannel scattering for three-body collinear systems is proposed. It is shown, that in this simple case the principle of quantum determinism in the general case breaks down and we…
In this work we build a theoretical framework for the transport of information in quantum systems. This is a framework aimed at describing how out of equilibrium open quantum systems move information around their state space, using an…
The motion of a nonlinearly oscilating partical under the influence of a periodic sequence of short impulses is investigated. We analyze the Schrodinger equation for the universal Hamiltonian. The idea about the emerging of quantum chaos…
Recent measures of nonclassical correlations are motivated by different notions of classicality and operational means. Quantum discord has received a great deal of attention in studies involving quantum computation, metrology, dynamics,…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
We consider the distribution of the (properly normalized) numbers of nodal domains of wave functions in 2-$d$ quantum billiards. We show that these distributions distinguish clearly between systems with integrable (separable) or chaotic…
Two major deviations from causality in the existing formulations of quantum mechanics, related respectively to quantum chaos and indeterminate wave reduction, are eliminated within the new, universal concept of dynamic complexity. The…
The study of chaos has long relied on computationally intensive methods to quantify unpredictability and design control strategies. Recent advances in machine learning, from convolutional neural networks to transformer architectures,…
We show that the main difference between classical and quantum systems can be understood in terms of information entropy. Classical systems can be considered the ones where the internal dynamics can be known with arbitrary precision while…
One of the major breakthroughs in science of the last (20th) century was building a bridge between the worlds of stochastic (random) systems and deterministic (dynamical) systems. It was started by the celebrated 1958 paper by…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to…
It is shown that quantum mechanics is a plausible statistical description of an ontology described by classical electrodynamics. The reason that no contradiction arises with various no-go theorems regarding the compatibility of QM with a…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…